Question: Simplify the following expression: $\dfrac{44a^4}{4a^5}$ You can assume $a \neq 0$.
Answer: $ \dfrac{44a^4}{4a^5} = \dfrac{44}{4} \cdot \dfrac{a^4}{a^5} $ To simplify $\frac{44}{4}$ , find the greatest common factor (GCD) of $44$ and $4$ $44 = 2 \cdot 2 \cdot 11$ $4 = 2 \cdot 2$ $ \mbox{GCD}(44, 4) = 2 \cdot 2 = 4 $ $ \dfrac{44}{4} \cdot \dfrac{a^4}{a^5} = \dfrac{4 \cdot 11}{4 \cdot 1} \cdot \dfrac{a^4}{a^5} $ $\phantom{ \dfrac{44}{4} \cdot \dfrac{4}{5}} = 11 \cdot \dfrac{a^4}{a^5} $ $ \dfrac{a^4}{a^5} = \dfrac{a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a} = \dfrac{1}{a} $ $ 11 \cdot \dfrac{1}{a} = \dfrac{11}{a} $